A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.

A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC transformations, to three distinct types. The analysis and the results should be helpful for finding different entanglement types in multipartite pure state systems.

A complete analysis of entangled triqubit pure states is carried out based on a new simple entanglement measure. An analysis of all possible extremally entangled pure triqubit states with up to eight terms is shown to reduce, with the help of SLOCC transformations, to three distinct types. The analysis presented are most helpful for finding different entanglement types in multipartite pure state systems.Entanglement is a fundamental concept that underpins quantum information and computation. [1−3] As a consequence, the quantification of entanglement emerges as a central challenge. Many authors have contributed to this topic, [4−23] among which the basic requirements for entanglement measures proposed in [4] provide with guidelines for its definition. In [6], Bennett et al defined stochastic local operations and classical communication (SLOCC) based on the concept of local operations assisted with classical communication (LOCC). Dür et al applied such an operation to a triqubit pure state system and found that triqubit states can be entangled at least in two inequivalent ways, [7] namely, in the GHZ form [24] or the W form. [7] In this Letter, we will use a recently proposed entanglement measure [23] for N -qubit pure states to analyze all extremally entangled triqubit pure states with the constrained maximization, and to see whether there are other inequivalent types of entanglement.In the following, based on the method used in [7], only entanglement properties of a single copy of a state will be considered. Therefore, asymptotic properties will not be discussed. At single copy level, it is well known that two pure states can always be transformed with certainty from each other by means of LOCC if and only if they are related by Local Unitary transformation (LU). [6] However, even in the simplest bipartite cases, entangled states are not always related by LU, and continuous parameters are needed to label all equivalence classes. Hence, it seems that one needs to deal with infinitely many kinds of entanglement. Fortunately, such arbitrariness has been overcome with the help of SLOCC. [7] According to [23], for a genuine entangled N -qubit pure state Ψ, the measure can be defined by